PeopleJessica Simpson shared the first photos of her baby, Maxwell Drew Johnson, with People magazine.

PeopleJessica Simpson shared the first photos of her baby, Maxwell Drew Johnson, with People magazine.

After what seemed like a long pregnancy, Jessica Simpson gave birth to her first child on May 1. Less than a month later, the first photos of little Maxwell Drew Johnson are already on the cover of People.

"From how I sleep to what I think about, Maxwell has definitely taken over everything!" the 31-year-old singer and entrepreneur told the magazine. "We stare at her all the time... We can't get enough!"

The cute little baby girl, born at 9 pounds, 13 ounces, appears to be sleepy in her first professional photo shoot, which People's assistant managing editor Kate Coyne unveiled on the "Today" show Wednesday morning.

"[Jessica's] on cloud nine," Coyne said. "She's really at peace. She's loving motherhood. There have been really no major bumps in the road. This is everything she dreamed it would be."

And, despite rumors that the girl's middle name came from Simpson's ex-husband Nick Lachey's brother Drew, Coyne explained that it's her fiancé Eric Johnson's middle name and his mother's maiden name.

Simpson and the former NFL football player reportedly sold the picture rights for more than $800,000 to the celebrity magazine, according to Fox News. The new issue of People hits newsstands on Friday.